219,096

2³ × 3² × 17 × 179

219,096 factors as 2^3 × 3^2 × 17 × 179. Its 48 positive divisors give a proper-divisor sum of 412,704, so this integer is abundant. The Collatz stopping time is 186 steps.

Prime Factor Structure

Factorization String 2^3 × 3^2 × 17 × 179

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 631,800

Proper Divisor Sum 412,704

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #219091 ← → #219097

Radix Representation

Decimal	219096
Binary	110101011111011000 (18 bits)
Octal	0o653730
Hexadecimal	0x357D8

Divisor Catalog (48)

1 2 3 4 6 8 9 12 17 18 24 34 36 51 68 72 102 136 153 179 204 306 358 408 537 612 716 1,074 1,224 1,432 1,611 2,148 3,043 3,222 4,296 6,086 6,444 9,129 12,172 12,888 18,258 24,344 27,387 36,516 54,774 73,032 109,548 219,096

Collatz Trajectory (186 steps to reach 1)

Iterative sequence n → n/2 (if even) or 3n+1 (if odd):

219,096 109,548 54,774 27,387 82,162 41,081 123,244 61,622 30,811 92,434 46,217 138,652 69,326 34,663 103,990 51,995 155,986 77,993 233,980 116,990 58,495 175,486 87,743 263,230 131,615 394,846 197,423 592,270 296,135 888,406 444,203 1,332,610 666,305 1,998,916 999,458 499,729 1,499,188 749,594 374,797 1,124,392 562,196 281,098 140,549 421,648 210,824 105,412 52,706 26,353 79,060 39,530 19,765 59,296 29,648 14,824 7,412 3,706 1,853 5,560 2,780 1,390

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